Dear Anne(Hà Lam).

I received your email last week, in which you asked me about my city New York in 2050. There are different ideas about this question. I thought it in a few days, and now I can give you two predictions.

Let's take a look at an optimis viewpoint. In 2050 New York will become a more liveable city than ever before for lots of reasons. The city authorities have built a very careful plan to promote self-driving electric taxis to deal with crowded public transport. In addition, the city dwellers are encouraged to use city's building roofs for gardens fertilised with compose in order to recycle rubbish and reduce pollution. The government will also build offshore windfarms to replace ageing electricity network.

On the other hand, pessimis people think that the city life won't be a safe place to live in because the government cannot control the use of guns, and therefore the crime rate will be higher. People's life will also continue to be threatened because of natural disasters such as floods, storms, earthquakes. The effects of global warming have great impacts on the city dwellers.

That's all about my answer to your question. I hope you will be satisfied with it, Nam.

Best wishes,

Wonie(Quyên)

tham khảo ạ

Dear Bich

Your last email asked me about my city Ha Noi in 2050. Well, but I'm busy and have no time to reply you soon. Today I am writing to you about that question. There are different ideas about this question. I thought about it in a few days, and now I can give you some predictions.

Let's take a look at optimis aspects. In 2050 Ha Noi will become a more modern city for lots of reasons. High technology has been applied in our lives. The robots will replace us for many jobs such as manufacturing, farming, etc. Smart cars which will be commonly used in the road. They will help human beings to decrease the accidents as well as traffic jams.

On the contrary, pessimis people think that the city life will be a dangerous place to live in because the environment is completely polluted. The effects of global warming have great impacts on the city dwellers, higher temperature in the summer and colder climate in the winter. There are a lot of means of transport so that emission from them cause air pollution. Our health will be threatened because of low air quality index.

That's all about my thoughts about your question. I hope you will be satisfied with it, Bich.

Best wishes,

Chau

Dear Liu!

Last time I told you that I had been thinking about pursuing higher education in the UK. I got started to learn the process of applying for a university in London some time ago. Now I have some questions for you. 

First, what is the procedure for applying for a student visa? Of course. I have to submit an application but what other documents are required? How long does it take me to obtain my student visa? It is important to plan time to wait for visa processing because the time between finding out I have been accepted to go and leaving may be very close together. Second, do 1 have to present my financial documents; for example proof of funds, to prove that I am able to pay for my education? And last, do I need to obtain the International Certificate of Vaccination? Is it required that I have certain vaccinations before I go? What are they? After all. can you make me a checklist: what I should bring and what I should leave at home? 

I wish you and your family the best. I look forward to hearing from you soon. 

                                                                                                     Regards, 

                                                                                                     Mai Anh

Mong cô duyệt bài ạ:

Dear Duc Son,

Last time I told you that I had been thinking about pursuing higher education in the UK. I got started to learn the process of applying for a university in London some time ago. Now I have some questions for you.

First, what is the procedure for applying for a student visa? Of course. I have to submit an application but what other documents are required? How long does it take me to obtain my student visa? It is important to plan time to wait for visa processing because the time between finding out I have been accepted to go and leaving may be very close together. Second, do 1 have to present my financial documents; for example proof of funds, to prove that I am able to pay for my education? And last, do I need to obtain the International Certificate of Vaccination? Is it required that I have certain vaccinations before I go? What are they? After all. can you make me a checklist: what I should bring and what I should leave at home?

I wish you and your family the best. I look forward to hearing from you soon.

Regards,

Dang Phong

\(2tan^2x-2\sqrt{3}tanx-3=0\)      

\(\orbr{\begin{cases}tanx=\frac{3+\sqrt{3}}{2}\\tanx=\frac{-3+\sqrt{3}}{2}\end{cases}}\)   

\(\orbr{\begin{cases}tanx=tana\\tanx=tanb\end{cases}}\)   Đặt \(tana=\frac{3+\sqrt{3}}{2};tanb=\frac{-3+\sqrt{3}}{2}\)   

\(\orbr{\begin{cases}x=a+k\pi\\x=b+k\pi\end{cases};k\in Z}\)    

\(\sqrt{3}cot^2x-\left(1+\sqrt{3}\right)cotx+1=0\)   

\(\orbr{\begin{cases}cotx=1\\cotx=\frac{\sqrt{3}}{3}\end{cases}}\)   

\(\Rightarrow\orbr{\begin{cases}tanx=1=tan\frac{\pi}{4}\\tanx=\sqrt{3}=tan\frac{\pi}{3}\end{cases}}\)   

\(\orbr{\begin{cases}x=\frac{\pi}{4}+k\pi\\x=\frac{\pi}{3}+k\pi\end{cases};k\in Z}\)

bang lon

Câu 2:

a) Điều kiện: \(x\ne-1\)

BPT tương đương:

\(\frac{\left(x+1\right)^2\left(\sqrt{x^2+2x+2}+1\right)}{x^2+2x+1}\ge4+2x\)

\(\Leftrightarrow\sqrt{x^2+2x+2}\ge3+2x\)

\(\Leftrightarrow3+2x< 0\left(h\right)\hept{\begin{cases}3+2x\ge0\\x^2+2x+2\ge9+12x+4x^2\end{cases}}\)

\(\Leftrightarrow x< -\frac{3}{2}\left(h\right)\hept{\begin{cases}x\ge-\frac{3}{2}\\-\frac{7}{3}\le x\le-1\end{cases}}\Leftrightarrow x\le-1\)

Kết hợp ĐK suy ra \(S_a=\left(-\infty;-1\right)\)

b) Hệ tương đương:

\(\hept{\begin{cases}\left(x^2+1\right)=y\left(x+y+2\right)\left(1\right)\\\left(x^2+1\right)\left(x+y-2\right)=5y\left(2\right)\end{cases}}\)

Ta thấy VP(1) = VT (1) = x² + 1 khác 0, vậy thì chia VT(2) và VP(2) cho VT(1) và VP (1), ta được:

\(x+y-2=\frac{5}{x+y+2}\Leftrightarrow\left(x+y\right)^2=9\Leftrightarrow\orbr{\begin{cases}x+y=3\\x+y=-3\end{cases}}\)

+) Nếu \(y=3-x\) thì (1) trở thành:

\(x^2+5x-14=0\Leftrightarrow\orbr{\begin{cases}x=2\\x=-7\end{cases}}\Rightarrow\orbr{\begin{cases}\left(x;y\right)=\left(2;1\right)\\\left(x;y\right)=\left(-7;10\right)\end{cases}}\)

+) Nếu \(y=-3-x\) thì (1) trở thành:

\(x^2-x-2=0\Leftrightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\Rightarrow\orbr{\begin{cases}\left(x;y\right)=\left(-1;-2\right)\\\left(x;y\right)=\left(2;-5\right)\end{cases}}\)

Vậy \(S_b=\left\{\left(2;1\right);\left(-7;10\right);\left(-1;-2\right);\left(2;-5\right)\right\}.\)

TH 4 bạn nữ hoặc 5 bạn nữ đứng liền nhau: 

Coi nhóm 4 bạn nữ là X, số cách sắp xếp nhóm X là: \(4!\)(cách)

Sắp xếp X, 1 bạn nữ còn lại và 4 bạn nam có:  \(6!\)(cách)

Xếp ngẫu nhiên 9 bạn có: \(9!\)(cách)

Vậy xác suất để không quá 3 bạn nữ đứng liền nhau là: \(\frac{9!-4!.6!}{9!}=\frac{20}{21}\)

Gọi tọa độ điểm $M$, $N$ lần lượt là $M\left(x_1;y_1\right),N\left(x_2;y_2\right)$.

Hệ số góc tiếp tuyến của $\left(C\right)$ tại $M$ và $N$ lần lượt là

$k_1=y^{\prime }\left(x_1\right)=-3{x_1}^2+6x_1-1$; $k_2=y^{\prime }\left(x_2\right)=-3{{}^{}}^{}$